Visual inspection

To think about this topic, let’s consider the examples of the Corine Land Cover (CLC) data for Tartu, Estonia in 2000 and 2018, and for Poznan, Poland in 2018:

We can start comparing the spatial patterns in these rasters just by looking at them: the land cover for Tartu in 2000 and 2018 looks similar, but it is different for Poznan in 2018 (much more urban areas, less forests). A comparison of Tartu in 2000 and 2018 suggests that urban areas have expanded into areas that were previously mostly covered by agricultural land. Visual inspection is a good starting point, as the human eye can detect multiple patterns that are not easily quantifiable. At the same time, it is subjective and may not be suitable for large datasets.

Generalization of the main aspects to consider

Alternatively, we can use quantitative methods to compare the spatial patterns in these rasters. Figure 1 shows general considerations when thinking about the properties of the methods for comparing spatial patterns in raster data.

flowchart TB
  A[Arbitrary regions] ---|Yes| B(Spatial context)
  A ---|No| C(Spatial context)
  B ---|Yes| D{{Outcome}}
  B ---|No| E{{Outcome}}
  C ---|Yes| F{{Outcome}}
  C ---|No| G{{Outcome}}
  D --> H([Single value])
  E --> I([Single value])
  F --> J([Single value]) 
  F --> K([Multiple values])
  F --> L([Raster]) 
  G --> M([Single value])
  G --> N([Multiple values])
  G --> O([Raster])
  
  style D stroke:transparent
  style E stroke:transparent
  style F stroke:transparent
  style G stroke:transparent

The first main aspect to consider when comparing spatial patterns in raster data is whether or not we are dealing with arbitrary regions. Working on overlapping (i.e., non-arbitrary) regions, e.g., CLC in Tartu in 2000 and 2018, allows for different approaches than working on arbitrary regions, e.g., CLC in Tartu in 2018 and Poznan in 2018. With non-arbitrary regions, each cell in one raster (or each cell in a moving window) can be compared to a corresponding cell in another raster. Thus, one possible outcome of the comparison is another raster, which highlights where the spatial patterns are similar or different. This is not possible with arbitrary regions, and the comparison usually includes spatial patterns of whole rasters.

The second main aspect to consider when comparing spatial patterns in raster data is whether the method used allows the integration of the spatial context of the analysis. A difference between the values of two cells is straightforward to calculate and interpret, but it does not consider the other local values. Alternatively, some methods use the spatial context of the analysis, e.g., by comparing the values in a moving window or a local neighborhood.

It is also worth noting that the comparison of spatial patterns in raster data can result in different types of data. For overlapping regions, the outcome can be a single value, multiple values, or a raster, and for arbitrary regions, it is usually a single value (multiple values are also possible, but often as a collection of single values’ results).

The above considerations can be applied to both continuous and categorical raster data, but the methods used for comparing spatial patterns in these two types of data are different.